Basic training in Mathematical Analysis.

I learned the method of Induction, sequences and calculating limits and continuity of real functions of real variable.

I learned the fundamental theorems and rules: Cauchy's Rule, Bolzano's Theorem, Lagrange's Theorem, Rolle's Theorem, Weirstrass' Theorem and Taylor's Theorem.

I learned integral calculus in R and the Fundamental Theorem of Calculus. In addition, I learned the formula of integration by parts and by substitution

Finally, I learned numerical series: geometric series, comparison criteria, absolutely convergent series and power series

I learned the basics of programming through Python. I was introduced to Matlab.

I learned the basics of imperative and recursive programming. I learned how to declare variables and types and how to define subroutines and functions.

I learned large-scale programming: object-based, layered modular programming method (eg: Hanoi Towers).

I performed a final project with object-oriented programming.

I gained notion of important algorithms in computer science.

I developed knowledge to know how to select the materials for a given engineering project.

I learned the mechanical properties of materials and the basics of composites and polymeric materials.

I understood the structures of materials, atomic diffusion in solids and solidification.

I learned to interpret phase balance diagrams.

Finally, I learned about materials processing technologies and how materials are recycled.

Developed the graphical representation capability associated with industrial systems and products.

I gained the ability to produce and transmit ideas using freehand drawing and CAD and geometric modeling techniques.

I learned the basics of technical drawing.

I made production drawings: descriptive memory, assembly drawings and parts drawings.

I learned the differential and integral calculus of functions of more than one real variable, including the fundamental theorems of calculus and applications to physics.

I also learned knowledge about Functions of Rn in Rm: limits, continuity, differentiability, partial derivatives, derivative of the composite function and Taylor's Theorem in Rn.

I understood the Inverse Function Theorem and Implicit Function Theorem. I learned to calculate conditioned extremes with Lagrange multipliers. I learned to calculate multiple integrals using Fubini's Theorem and Change of Variables Theorem.

I understood how to calculate line integrals: Scalar and vector field integrals. Fundamental Theorem of Calculus for Line Integrals. Green's Theorem. I figured out how to calculate surface integrals. Stokes' theorem. Gauss Theorem.

I understood the systemic and integrated nature of how organizations work.

I learned to assess the multidisciplinarity and resources necessary for the functioning of organizations. I was introduced to the economic environment (Macroeconomics,Microeconomics).

I learned about financial information. I learned to make a balance sheet, an income statement, calculate costs and analyze economic and financial ratios.

I learned about how to analyze investment projects. Understood how to calculate current and future values of cashflows and refresh rates.

I also learned about strategic management (External Analysis, Internal Analysis and Strategy Formulation).

Finally, I had a brief introduction to marketing (Targeting, Targeting, Positioning and Marketing Mix).

Acquired essential concepts in a technical design specification, including manufacturing and control specifications.

I learned knowledge of materials selection and manufacturing processes and their indication in the technical specification and drawings.

I learned functional dimensioning, dimensional tolerances of dimensions and deviations, types of fit and geometric tolerances.

I also learned to create references in technical drawings, the different manufacturing processes and everything about surface finishes.

Finally, I learned how to represent welds, specify standard components and do design documentation.

I learned the basics of classical mechanics, wave phenomena, and special relativity.

I understood kinematics, dynamics, conservation laws and space-time symmetries.

In addition, I learned how the movement of a rigid body works and how to calculate torques and moments of inertia.

Finally, I learned simple harmonic oscillations and oscillations with forced friction, waves and fluids.

The course made me understand the structure, properties and transformations of materials in general.

I learned the basics of polyelectronic atoms, the model of molecular orbital theory (TOM/CLOA) and polyatomic molecules.

I understood the intermolecular forces and properties of molecular compounds. I covered covalent crystals, metallic crystals and ionic crystals.

I discussed the mechanical properties of metals, polymers, ceramics and composite materials and the electrical properties and band structure of metallic, covalent and ionic crystals.

Finally, I understood chemical kinetics, chemical thermodynamics and application to equilibrium.

I acquired knowledge on the following subjects: vector spaces, linear transformations, Euclidean spaces, values and eigenvectors.

I learned Gauss elimination method, matrices and vectors, matrix inversion, linear spaces and linear transformations.

I also understood the bases and dimensions, the core and counter-domain of a linear transformation.

I learned internal products and standards, orthogonal bases and Gram-Schmidt orthogonalization. Orthogonal complements and projections. Line and plane equations. Least squares.

Finally, I learned determinants, eigenvalues and vectors, invariant subspaces and matrix diagonalization. Hermitian, anti-hermitian and unitary transformations. Quadratic forms.

I understood the finite limitation of numerical algorithms. I learned to work with error estimates and understood the propagation of errors in algorithms.

I learned to interpolate and extrapolate data by interpolation and least squares, and I realized how to apply it to data science and experimental measurements. In addition, I learned to approximate, derive and integrate functions by numerical methods and understood how to apply them to non-elementary functions.

I learned to solve equations and nonlinear systems by numerical methods. I realized how to approximate the solution of ordinary differential equations, including systems.

I also understood how to approximate the solution of problems with partial differential equations.

I developed elementary computational projects in Matlab applying the knowledge to various engineering and graphic visualization problems.

I learned the statics of rigid bodies: Moment of a Force about a Point and an Axis; Moment of a Binary; Equivalent Systems of Forces; Equilibrium of a Rigid Body in Two and Three Dimensions; Loads Distributed on Beams.

I learned the statics of rigid bodies: Moment of a Force about a Point and an Axis; Moment of a Binary; Equivalent Systems of Forces; Equilibrium of a Rigid Body in Two and Three Dimensions; Loads Distributed on Beams.

I learned the method of virtual jobs: Real Machines; Work of a Force; Potential Energy and Balance; Stability. I learned several concepts on geometry of masses: Center of Mass; Moments of Area and Inertia; Inertia Tensor.

Finally, the kinematics of rigid bodies were studied: Rotation; Flat Movement; Instant Center of Rotation; Absolute and Relative Acceleration; Movement of a Particle in Three Dimensions Relative to a Rotating Axis System.

I understood the basic concepts of electrostatics: Coulomb's law; electrostatic field; overlap principle; field and potential; electric dipole; Gauss' law; capacity and capacitors; dielectrics and polarization; electricity.

I studied the concept of stationary electric current: current density and intensity; load continuity; Ohm's, Joule and Kirchhoff's laws.

I studied the variable electromagnetic field (e.m.) and what are its applications: induction and Faraday's law; electrical transformers, motors and generators; displacement current; energy e.m.; RC, RL and RLC circuits.

I studied Maxwell's equations and e.m. waves: monochromatic plane waves; wave energy and intensity. Lastly, I learned optical concepts: character e.m. from light; dispersion, polarization, reflection, interference and diffraction; geometric optics, reflection and refraction; Fresnel equations and Fermat's principle.

I learned to solve elementary ordinary differential equations (ODEs) and to solve linear differential equations and systems of equations: integration factors; existence, uniqueness and continued dependence on ODE solutions; constant variation formula; ODEs of order > 1; Laplace transformations.

I studied the Gauss and Stokes Theorems, the general divergence and curl properties of vector fields, and their applications. I learned to calculate surface integrals of scalar and vector fields.

I learned to solve elementary linear 1st and 2nd order partial differential equations (PDEs): Wave, heat, Laplace and Poisson equations.

Finally, I studied the general and convergence properties of Fourier series, Fourier transformation and their applications.

I learned the concept of stress: Normal and cut-off stresses; Allowable stress and safety factor. In addition, I realized the concept of deformation: Normal and shear deformations; Stress-strain diagram; Elastic behavior; Hooke's Law; Axial stress. Elastic deformation of axially loaded bar. Statically indeterminate bars. Overlay method. Problems involving temperature variations.

I understood torsion: Torsional deformation of shafts of circular section in elastic regime; torsion tension. Torsion angle. Statically indeterminate veins.

I understood bending: Diagrams of shear stress and bending moment. Normal bending stress. Non-symmetrical bending. Shear stress due to shear stress. Shear stress in thin-walled profiles. Cut center.

I studied problems with stresses due to combined loads and learned the deformation of beams: Elastic curve. Calculation of the deformation of beams. Statically indeterminate beams.